Henning–Oellermann–Swart conjecture on the Steiner k-diameter and Steiner k-radius

Let $k\geq 2$ be an integer, and let $G$ be a connected graph with order at least $k$. The Steiner $k$-diameter $Sd_k(G)$ and Steiner $k$-radius $Sr_k(G)$ are defined using Steiner distances over $k$-vertex subsets of $G$.

Henning–Oellermann–Swart conjecture.

$$Sd_k(G)\leq\dfrac{2(k+1)}{2k-1}Sr_k(G).$$

Henning, Oellermann and Swart proposed this bound; the paper states that it has been proved for $k=3$ and $k=4$, while the general case remains open.